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Vector Applications

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Vector Applications

Created by: Jeffrey Bivin

Edited by: Aaron Rogers

jeff.bivin@lz95.org

Last Updated: February 14, 2011

Find the component form of the vector that represents the velocity of an airplane descending at a speed of 150 mph at an angle of 30o below the westward horizontal.

210o

30o

150 mph

An airplane is traveling at a speed of 600 mph with a bearing of N35oW at a fixed altitude and no wind. As the plane crosses the Mississippi river, it encounters a wind blowing with a velocity of 60 mph in the direction of N40oE. What is the resultant speed and direction of the plane?

60 mph

125o

35o

result

40o

50o

600 mph

60 mph

600 mph

wind

result

plane

125o

35o

result

40o

50o

600 mph

60 mph

600 mph

wind

result

plane

Joey is playing tug of war with his two best friends. He is pulling with a force of 60N at 210o.Simon exerts a force of 30N at 45o. Austin exerts a force as well. To achieve equilibrium and thus, not lose the game, what is the force Austin must exert and at what angle?

210o

45o

30 N

60 N

210o

45o

30 N

60 N

210o

45o

30 N

60 N

22o

49o

10000 lbs

A 10,000 pound object is suspended on a wire tied to two poles. The angle between the horizontal and the wire to the shorter pole is 22o. The angle between the horizontal and the wire to the taller pole is 49o. Find the tension in the cable to each pole.

158o

f1

f2

22o

49o

10000 lbs

f1

f2

22o

49o

10000 lbs

f1

f2

Put in a Matrix and use A-1B

or can use RREF

500 lbs

f

67o

23o

500 lbs

Normal Vector

Gravity

1500 lbs

f

72o

18o

1500 lbs

A mover exerts a force of 55 pounds in a horizontal direction on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate.

55 lbs

20 ft.

A mover exerts a force of 55 pounds at an angle of 45o below the horizontal on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate.

45o

55 lbs

20 ft.

A sled is to be pulled by a rope at a 37o angle above the horizontal with a force of 63 lbs.. Find the amount of work done to move the sled 15 feet.

63 lbs

37o

15 ft.

A mover exerts a horizontal force of 35 pounds on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate.

40 ft.

35 lbs

13o

A mover exerts a force of 35 pounds parallel to the ramp on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate.

35 lbs

13o

Note: The force is in the same direction of the movement. Therefore, all the force is moving the crate.

A mover exerts a force of 35 pounds on a crate at an angle of 20o below the horizontal as it is pushed up aramp that is 50 feet long and inclined at an angle of 23oabove the horizontal. Find the work done on the crate.

50 ft.

20o

35 lbs

23o

The following slides are the same examples previously examined that calculate the work needed to move an object. However, an alternative method is demonstrated.

A mover exerts a force of 55 pounds at an angle of 45o below the horizontal on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate.

45o

55 lbs

45o

f

A sled is to be pulled by a rope at a 37o angle above the horizontal with a force of 63 lbs.. Find the amount of work done to move the sled 15 feet.

63 lbs

37o

f

A mover exerts a horizontal force of 35 pounds on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate.

35 lbs

13o

f

13o

A mover exerts a force of 35 pounds parallel to the ramp on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate.

35 lbs

13o

Note: The force is in the same direction of the movement. Therefore, all the force is moving the crate.